Answer the following questions:

If interest rates rise, do bond prices rise or fall?

If the bond yield to maturity is greater than the coupon, is the price of the bond greater or less than $1000?$

If the price of a bond exceeds $1000,$ is the yield to maturity is likely to be greater or less than the coupon?

Do high$-$coupon bonds generally sell at higher or lower prices than low$-$coupon bonds $($assuming all other things equal$)?$

Assume all other things equal and then if interest rates change, do the prices of high$-$coupon bonds change proportionately more than that of low$-$coupon bonds?